Entitlement to holiday pay depends on whether or not your freelancer will be defined as a worker. Employment status is a very complex piece of legislation and the entitlement of this person to holiday would depend on the contract and what HRMC considers their employment status to be. The nature of the working relationship can also change over time into something other than what was originally intended to be.
If this person has worked consistent hours each week and provides a particular personal service which they cannot easily turn down or pass on to someone else to complete, then there is a chance that this person may be classed as a worker and so entitled to holiday pay.
Generally, a truly self-employed worker would not be entitled to payment for a holiday period although it is always best to spell this out clearly within the contract for services between you both so that the intentions are clear. However, each individual case is different and fact sensitive so further advice should be sought in order to properly clarify your particular case.